[isaac]

If it's not backfiring out of the intake and exhaust, you're not 180 degrees off with cam timing compared to ignition.

This is simple stuff, probably solved by either

A) You need a new spark plug. Fuel fouling will not show up in a traditional spark test. The plug will fire normally outside the cylinder. Inside the high pressure cylinder it won't fire right. This sometimes can be fixed by just taking a torch to the plug (though sometimes it's too messed up). If you heat it with a torch, install it right away and then crank it's much more likely to fire, but not guaranteed.

B) The carb got installed wrong. This can manifest itself in all sorts of ways, but mostly it'll be at start and idle. The extremely easy way to check this is to first put a new plug in there, then spray starting fluid (or carb cleaner, or brake cleaner, or hold a gas soaked rag over the intake) and crank it. If it fires, then the carb is your problem.

C) There's something else causing over/under fueling. Either you forgot to hook up the vacuum hose between the carb and the fuel valve on the tank, the carb isn't sealed to the engine, or the carb gummed up while it was sitting or the fuel valve in the carb is stuck. Small engines have small carb jets and gum up extremely easily. Again this is something easily ruled out by spraying carb spray and cranking.

D) The cam is off by a tooth one way or the other. But you'd probably get at least a kick while cranking. If it's off by more than a tooth or two it'll probably bend valves.

E) Gas-washed cylinder walls. Metal in cylinder walls absorbs oil. That micrometer-thick slick of oil helps with compression. If you had too much fuel going through the engine, especially after it had sat for a long time, the cylinder walls can get gas-washed and the engine will have less compression than normal. This can be rectified quickly by squirting some oil into the plug hole, installing a new plug (notice how I keep repeating that), spraying carb fluid into the intake and cranking.

If you check all those and it's still not firing, I wouldn't be shocked if the engine was put back together wrong. But if you really put it back together so wrong that it won't fire but somehow still sounds normal while cranking, compresses audibly every other rotation, and doesn't backfire through the intake or exhaust, then I'd say you're a tooth off somewhere.

The only way you could get the ignition wrong but the cam timing right is if you messed with the ignition pickup inside the right side crankcase cover, which I doubt you did. Did you hook up the ignition coil wiring backward? I don't know if that makes a difference but it may have a one-way transistor in there. What is possible is that you got the ignition right but the cam 180 degrees off. If that happened, as I've said, you'd be backfiring out of the intake and exhaust because the plug would fire just as the exhausts were closing and the intakes opening (during overlap).

I had an undiagnosable no-start on mine once that was cured by a new carb slide of all things. Went from barely running to running perfectly with one part, many months of aggravation later.